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math.AP2025
Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems
Boumediene Abdellaoui, Somia Atmani, Kheireddine Biroud +1
In the first part of this paper, we prove the global regularity, in an adequate parabolic Bessel-Potential space and then in the corresponding parabolic fractional Sobolev space, o…
math.AP2025
Fractional elliptic reaction-diffusion systems with coupled gradient terms and different diffusion
Somia Atmani, Kheireddine Biroud, Maha Daoud +1
In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of . The diffusion…
math.AP2017
Nonlinear fractional elliptic problem with singular term at the boundary
Boumediene Abdellaoui, kheireddine Biroud, Ana Primo
Let be a bounded regular domain, and . We consider $$ (P)\left\{ \begin{array}{rcll} (-Δ)^s u &= & \frac{u^{q}}{d^{2s}} & \text{ in }Ω, \\ u &…